Aspects of this question have been thoroughly treated in *The Classification of Finite Simple Groups*, Number 3, by Gorenstein-Lyons-Solomon, AMS, 1994: see especially their Table 3.3.1 for the Chevalley groups.   In your notation (which differs somewhat from theirs), the $p$-rank is $16a$.   This gives only the rank of a maximal *elementary* abelian $p$-subgroup, however.